The Kepler Problem: Orbit Cones and Cylinders

2012/01/23 by Terry R. McConnell, McConnell, Terry R.
Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Historical Astronomy and Related Studies #History and Developments in Astronomy #Relativity and Gravitational Theory #physics.class-ph

paper · pdf · doi:10.48550/arxiv.1201.4713

arxiv created 2012/01/23 · openalex publication_date 2012/01/23 · arxiv updated 2012/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Planetary orbits, being conic sections, may be obtained as the locus of intersection of planes and cones. The planes involved are familiar to anyone who has studied the classical Kepler problem. We focus here on the cones.

Related

• Revisiting Kepler: new symmetries of an old problem
• Elementary Solution of Kepler Problem (and a few other problems)
• Yet another approach to the inverse square law and to the circular character of the hodograph of Kepler orbits
• Projective deduction of the non-trivial first integral to the Euler problem: an explicit computation
• Orbit Elements from Kepler Solutions in Projective Coordinates